Question: Solve for $x$ and $y$ using elimination. ${-2x+4y = 6}$ ${2x+5y = 30}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $9y = 36$ $\dfrac{9y}{{9}} = \dfrac{36}{{9}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-2x+4y = 6}\thinspace$ to find $x$ ${-2x + 4}{(4)}{= 6}$ $-2x+16 = 6$ $-2x+16{-16} = 6{-16}$ $-2x = -10$ $\dfrac{-2x}{{-2}} = \dfrac{-10}{{-2}}$ ${x = 5}$ You can also plug ${y = 4}$ into $\thinspace {2x+5y = 30}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(4)}{= 30}$ ${x = 5}$